Eddy-current losses in finite sections of solid iron under saturation

The predetermination of eddy-current losses in solid iron due to an alternating magnetic field under saturation is a problem of great complexity. The problem is particularly difficult when the solid iron section is of finite dimensions. The object of the paper is to present a solution for the two-dimensional problem, taking into account the effect of saturation. The nonlinearity of the mean magnetisation curve is seen as producing a phase difference between the equivalent sinusoids of the magnetic intensity and the induction, in a way similar to hysteresis. This method of linearisation is carried out by introducing complex magnetic permeability, which obviously implies the substitution of the nonsinusoidal periodic functions of the magnetising force and the induction by equivalent sinusoids. The degree of saturation for any mean magnetisation curve is accounted for by the argument of the complex permeability. This concept leads to linearised differential Maxwell equations and provides a rigorous solution for losses in a two-dimensional problem. The analysis is applied to two different magnetic materials of finite sections and is verified against available experimental results. An interesting feature of the paper is that the results for the eddy-current losses are presented in a nondimensional form for extreme conditions of saturation. The table of computed results will be useful for a designer.